A367491 Lexicographically least increasing sequence, starting with 2, such that no two terms (possibly identical) sum to a Fibonacci number.

2, 5, 7, 9, 10, 13, 15, 18, 20, 22, 23, 26, 28, 30, 31, 34, 36, 38, 39, 41, 43, 44, 47, 49, 52, 54, 56, 57, 60, 62, 64, 65, 68, 70, 73, 75, 77, 78, 81, 83, 85, 86, 89, 91, 93, 94, 96, 98, 99, 102, 104, 107, 109, 111, 112, 115, 117, 119, 120, 123, 125, 127, 128

Offset: 1

Author

Jeffrey Shallit, Nov 20 2023

Keywords

• nonn

Comments

There is an 8-state Fibonacci automaton that accepts the Zeckendorf representation of n if and only if n belongs to the sequence.

Examples

			6 is not in the sequence, since if it were, 6+2 = 8, a Fibonacci number.
		

Crossrefs

Cf. A005652, A005653. This sequence allows the same term to be used twice in the sum, whereas in the other two sequences, the terms must be distinct.